8x^2+10x-68=0

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Solution for 8x^2+10x-68=0 equation: 


Simplifying
8x2 + 10x + -68 = 0

Reorder the terms:
-68 + 10x + 8x2 = 0

Solving
-68 + 10x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-34 + 5x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-34 + 5x + 4x2)' equal to zero and attempt to solve:

Simplifying
-34 + 5x + 4x2 = 0

Solving
-34 + 5x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-8.5 + 1.25x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 1.25x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 1.25x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 1.25x + x2 = 0 + 8.5
1.25x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
1.25x + x2 = 8.5

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 8.5 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 8.5 + 0.390625

Combine like terms: 8.5 + 0.390625 = 8.890625
0.390625 + 1.25x + x2 = 8.890625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 8.890625

Calculate the square root of the right side: 2.98171511

Break this problem into two subproblems by setting 
(x + 0.625) equal to 2.98171511 and -2.98171511.


Subproblem 1
x + 0.625 = 2.98171511

Simplifying
x + 0.625 = 2.98171511

Reorder the terms:
0.625 + x = 2.98171511

Solving
0.625 + x = 2.98171511

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 2.98171511 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 2.98171511 + -0.625
x = 2.98171511 + -0.625

Combine like terms: 2.98171511 + -0.625 = 2.35671511
x = 2.35671511

Simplifying
x = 2.35671511


Subproblem 2
x + 0.625 = -2.98171511

Simplifying
x + 0.625 = -2.98171511

Reorder the terms:
0.625 + x = -2.98171511

Solving
0.625 + x = -2.98171511

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -2.98171511 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -2.98171511 + -0.625
x = -2.98171511 + -0.625

Combine like terms: -2.98171511 + -0.625 = -3.60671511
x = -3.60671511

Simplifying
x = -3.60671511


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.35671511, -3.60671511}
Solution
x = {2.35671511, -3.60671511}

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